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# 24 - 16:22:59 CS 61B Lecture 24 Wednesday Todays reading...

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03/18/09 16:22:59 1 24 CS 61B: Lecture 24 Wednesday, March 18, 2009 Today’s reading: Goodrich & Tamassia, Chapter 7. ROOTED TREES ============ A _tree_ consists of a set of nodes and a set of edges that connect pairs of nodes. A tree has the property that there is exactly one path (no more, no less) between any two nodes of the tree. A _path_ is a connected sequence of zero or more edges. In a _rooted_ tree, one distinguished node is called the _root_. Every node c, except the root, has exactly one _parent_ node p, which is the first node traversed on the path from c to the root. c is p’s _child_. The root has no parent. A node can have any number of children. Some other definitions: - A _leaf_ is a node with no children. - _Siblings_ are nodes with the same parent. - The _ancestors_ of a node d are the nodes on the path from d to the root. These include d’s parent, d’s parent’s parent, d’s parent’s parent’s parent, and so forth up to the root. Technically, the ancestors of d also include d itself, which makes you wonder about d’s sex life. The root is an ancestor of every node in the tree. - If a is an ancestor of d, then d is a _descendant_ of a. - The _length_ of a path is the number of edges in the path. - The _depth_ of a node n is the length of the path from n to the root. (The depth of the root is zero.) - The _height_ of a node n is the length of the path from n to its deepest descendant. (The height of a leaf node is zero.) - The height of a tree is the depth of its deepest node = height of the root.

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24 - 16:22:59 CS 61B Lecture 24 Wednesday Todays reading...

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